阻抗边界条件下Maxwell方程的传输特征值问题  

Transmission Eigenvalue Problem of Maxwell’s Equations with Impedance Boundary Condition

作　　者：吴雪娇 刘立汉 汪晓青 WU Xuejiao;LIU Lihan;WANG Xiaoqing(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2023年第3期114-121,共8页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金青年项目(No.12001075);重庆市自然科学基金面上项目(No.cstc2020jcyj-msxmX0167);重庆市教育委员会科学技术研究项目(No.KJZD-K202100503,No.KJQN201900544);重庆市留学人员回国创新类项目(No.cx2021061,No.cx2019022);重庆师范大学青年拔尖人才培育计划(No.02030307/0052);重庆市巴渝学者计划(No.BYQNCS2020002);重庆市高校创新研究群体项目(No.CXQT20014)。

摘　　要：【目的】讨论反散射问题的研究中起着关键作用的传输特征值问题。【方法】利用边界积分方程方法,研究了可穿透、非磁性和非均匀介质中带有阻抗边界条件的Maxwell方程的传输特征值问题。【结果】构造了阻抗-磁边界迹算子,并用边界积分算子表示阻抗-磁边界迹算子。【结论】证明了一种边界积分算子的强制性,以及另一种边界积分算子的紧性,进一步得出阻抗-磁边界迹算子的差算子是指数为0的Fredholm算子且解析。[Purposes]The transmission eigenvalue problem is very important for inverse problems.[Methods]The transmission eigenvalue problem of Maxwel’s equations with impedance boundary condition in penetrable,nonmagnetic and nonuniform media was studied by using the boundary integral equation method.[Results]The impedance-magnetic boundary trace operator was constructed,and the impedance magnetic boundary trace operator was expressed by the boundary integral operator.[Conclusions]It is proved that one kind of boundary integral operator is coercive,another kind of boundary integral operator is compact,and the difference operator of impedance magnetic boundary trace operator is a Fredholm operator with index zero and analytic.

关 键 词：边界积分方程方法 传输特征值问题 阻抗-磁边界迹算子 FREDHOLM算子 

分 类 号：O221.6[理学—运筹学与控制论]